Roberto Mancini believes Manchester City's transfer activity over the next five days will shape their defence of the Premier League title, after the champions escaped with a fortunate draw at Liverpool.

City required an 80th-minute equaliser by Carlos Tevez to rescue a point at Anfield, the Argentina striker having received a gift from the Liverpool defender Martin Skrtel for his 100th goal in English football. Skrtel and Luis Suárez had twice given Liverpool the lead in Brendan Rodgers's first home league game as manager, as the Anfield club responded impressively to their calamitous opening day at West Bromwich Albion.

For Mancini, however, another unconvincing display from his side – though he insisted it merited a point – prompted the Italian to renew appeals for the world's wealthiest club to strengthen his squad before the transfer window closes on Friday.

City are close to making Scott Sinclair, the Swansea City winger, their second signing of the summer after the £12m recruitment of Jack Rodwell, but Mancini claimed there is an urgent need for further additions.

The City manager, who denied a report that he will quit the club next summer if there is a repeat of this window's transfer problems, said: "We need to bring players in and we have five days in which to do it. We have to work very hard in these four or five days. It will be a long week for us."

Asked if the next five days will shape City's season, Mancini said: "Yes. We have our targets and we will go for them in the next five days. How many? Ten, 15? [Daniel] Agger was never our target. Sinclair, maybe. We have five days." Despite Mancini's denials, Liverpool are understood to have rejected a £20m offer from City for Agger two weeks ago.

The City manager defended his decision to deploy a three-man defence at Anfield and claimed the free-kick that produced Suárez's goal – awarded for a handball against Rodwell – should not have been given: "It was the same as the penalty [in the League Cup semi-final] that was awarded against us here last year. It was not a penalty then and it was not a free-kick now.

"We had three at the back and for 30 minutes we pushed Liverpool into their own half. We should have scored then and we had three or four chances to do that. I am happy with this system and sometimes we will use it. Games are always difficult at Anfield. Then we conceded a goal from their first corner and something changed.

"We wanted to win but we were 1-0 down and then 2-1 down and we did not deserve to lose this game because we played well. In the end, I think this was a good result."

Liverpool lost Lucas Leiva to a thigh injury after four minutes but, with the recent £15m signing Joe Allen outstanding in central midfield, and 17-year-old Raheem Sterling impressing on his full league debut, Rodgers's only disappointment was the final result. "The best side out there didn't win," he said.

"I'm very happy with our progress. Our attitude and application has been great. We had a one-off at West Brom but apart from that we have shown great resilience and perseverance. Day in, day out, I am seeing improvements in our game and tactically they played with a terrific plan today."

For the second week running, Liverpool were punished for trying to play their way out of defence but Rodgers insisted: "It is not frustrating. It is all part of the journey. I commend the players' courage on the ball. The easiest thing is to get the keeper to smash the ball up the pitch and then the opposition have the ball and then they are on the attack again.

"Martin was immense, he scored with a wonderful header. And obviously he has been a real stalwart in the short period of time I have been in here. If we are to dominate games we need players with the courage to have the ball and Martin was very courageous so there is no blame on him."

The Liverpool manager started with Sebastián Coates at centre-half and Sterling on the right wing instead of Jamie Carragher and Stewart Downing, respectively. On the teenager's display, he said: "It was an easy decision. I said when I first came in here that I'll judge people not on their status or what they have done but what I see here and now in front of me.

"He is a young player who has improved every single day since I came in here."